
The Riemannian Gauss-Newton algorithm under the embedded geometry (RGN (E)) is given in Algorithm REF , where \(R^E(\cdot )\)  is a retraction from \( T_{{\cal X}}{\cal M}_{\mathbf {r}}\)  to \({\cal M}_{\mathbf {r}}\) . A typical retraction is [1]}, [2]}
\(R^E_{{\cal X}}\left(\xi \right)= \operatorname{TT-SVD}\left({\cal X}+\xi \right),\) 
